# Brightland Tech manufactures computer control boards for other manufac- turers of consumer goods such as microwave ovens,

## Question:

Brightland Tech manufactures computer control boards for other manufac- turers of consumer goods such as microwave ovens, toys, and flat screen monitors. Brightland's product is intended for finished goods that compete in the lower cost end of those markets, and so Brightland was unhappy to learn that its biggest rival announced a 100%, 2-year warranty on all its control boards, offering to pay its clients the repair or return costs of a finished good if the control board was the source of its failure. Brightland Tech customers are now asking Brightland to match that offer to keep their business. Brightland knows that any one of its inexpensive control boards is 98% reliable during its first year of operation, but that reliability drops to 97% during its second year of operation and then to 92% during its third year of operation. Brightland has the option of "twinning" the control board by installing two of the semiconductor processors that are the source of control board failure. The second processor would be redundant to the single processor in its current design, taking over instantly if the first processor were to fail. However, adding a second identical processor will increase Brightland's production costs and erode its profit margins.

Questions

1. What is the reliability of one of Brightland's computer control boards across its first 3 years of operation? In other words, what is the probability it will still be operating at the end of its third year?

2. If Brightland Tech agrees to offer a 2-year warranty covering its control boards, what is the chance that a control board will create a warranty expense during its first 2 years of operation?

3. Suppose Brightland installs a redundant processor on each control board, as described earlier. What is the reliability of the control board during its first year of operation?

4. Suppose Brightland installs a redundant processor on each control board, as described earlier. If the first processor remains operational at the end of the first year, what is the reliability of the control board during its second year of operation?

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